Bayesian Optimization
Description
Bayesian Optimization of Hyperparameters.
Usage
1 2 3 
Arguments
FUN 
The function to be maximized. This Function should return a named list with 2 components. The first component "Score" should be the metrics to be maximized, and the second component "Pred" should be the validation/crossvalidation prediction for ensembling/stacking. 
bounds 
A named list of lower and upper bounds for each hyperparameter. The names of the list should be identical to the arguments of FUN. All the sample points in init_grid_dt should be in the range of bounds. Please use "L" suffix to indicate integer hyperparameter. 
init_grid_dt 
User specified points to sample the target function, should
be a 
init_points 
Number of randomly chosen points to sample the target function before Bayesian Optimization fitting the Gaussian Process. 
n_iter 
Total number of times the Bayesian Optimization is to repeated. 
acq 
Acquisition function type to be used. Can be "ucb", "ei" or "poi".

kappa 
tunable parameter kappa of GP Upper Confidence Bound, to balance exploitation against exploration, increasing kappa will make the optimized hyperparameters pursuing exploration. 
eps 
tunable parameter epsilon of Expected Improvement and Probability of Improvement, to balance exploitation against exploration, increasing epsilon will make the optimized hyperparameters are more spread out across the whole range. 
kernel 
Kernel (aka correlation function) for the underlying Gaussian Process. This parameter should be a list that specifies the type of correlation function along with the smoothness parameter. Popular choices are square exponential (default) or matern 5/2 
verbose 
Whether or not to print progress. 
... 
Other arguments passed on to 
Value
a list of Bayesian Optimization result is returned:

Best_Par
a named vector of the best hyperparameter set found 
Best_Value
the value of metrics achieved by the best hyperparameter set 
History
adata.table
of the bayesian optimization history 
Pred
adata.table
with validation/crossvalidation prediction for each round of bayesian optimization history
References
Jasper Snoek, Hugo Larochelle, Ryan P. Adams (2012) Practical Bayesian Optimization of Machine Learning Algorithms
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  # Example 1: Optimization
## Set Pred = 0, as placeholder
Test_Fun < function(x) {
list(Score = exp((x  2)^2) + exp((x  6)^2/10) + 1/ (x^2 + 1),
Pred = 0)
}
## Set larger init_points and n_iter for better optimization result
OPT_Res < BayesianOptimization(Test_Fun,
bounds = list(x = c(1, 3)),
init_points = 2, n_iter = 1,
acq = "ucb", kappa = 2.576, eps = 0.0,
verbose = TRUE)
## Not run:
# Example 2: Parameter Tuning
library(xgboost)
data(agaricus.train, package = "xgboost")
dtrain < xgb.DMatrix(agaricus.train$data,
label = agaricus.train$label)
cv_folds < KFold(agaricus.train$label, nfolds = 5,
stratified = TRUE, seed = 0)
xgb_cv_bayes < function(max.depth, min_child_weight, subsample) {
cv < xgb.cv(params = list(booster = "gbtree", eta = 0.01,
max_depth = max.depth,
min_child_weight = min_child_weight,
subsample = subsample, colsample_bytree = 0.3,
lambda = 1, alpha = 0,
objective = "binary:logistic",
eval_metric = "auc"),
data = dtrain, nround = 100,
folds = cv_folds, prediction = TRUE, showsd = TRUE,
early.stop.round = 5, maximize = TRUE, verbose = 0)
list(Score = cv$dt[, max(test.auc.mean)],
Pred = cv$pred)
}
OPT_Res < BayesianOptimization(xgb_cv_bayes,
bounds = list(max.depth = c(2L, 6L),
min_child_weight = c(1L, 10L),
subsample = c(0.5, 0.8)),
init_grid_dt = NULL, init_points = 10, n_iter = 20,
acq = "ucb", kappa = 2.576, eps = 0.0,
verbose = TRUE)
## End(Not run)

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